Year 8 Revision Worksheets

Year 8 Revision Worksheets

Advice: For these revision worksheets, write your answers on a separate piece of paper and look up the answers when you’re finished. Did you get some questions wrong? If so, determine where you went wrong and come back to the questions another day to try and get full marks.

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Fractions

Give answers as mixed numbers where appropriate.

a) 12+13=

b) 145+259=

c) 314-25=

d) 25×35=

e) 412×312=

f) 2×45=

g) 37×9=

h) 1403×614=

i) 8÷13=

j) 13÷12=

k) 412÷43=

l) 513÷134=

m) 114÷2532=

n) -14--22=

o) 1-54=

p) 2--342=

q) 3--133=

Converting between decimals and fractions

a) 1.62 as a percentage:
______

b) 68% as a decimal:
______

c) 0.72 as a fraction in its simplest form: ______

d) 0.4 as a fraction in its simplest form: ______

e) 1.125 as a fraction in its simplest form:
______

f) Use long division to find the exact value of 58.
______

g) Use long division for find the exact value of 364.
______

h) Use long division to find 17 to 3dp.
______

i) Find 511 to 3dp.
______

j) Find 729 to 5dp.
______

Pythagoras Theorem

Find the sides labelled with a variable. When appropriate, give your answers in both decimal and surd form.

The following are more challenging:

Algebraic Simplification

Simplify the following

a) 9-3x+5x

b) x2+2x+3-x

c) x2+2xy+3z-2xy

d) 2x×3y

e) 6xy×3yz

f) 12z×2xz×x2

g) 3x9x2

h) 8x2y2xy2

i) xy2

j) x2y2

k) 2(x+2)

l) 9x-2+x(2-x)

m) 2xy2xy

n) x-y-(y-x)

o) 2x2x-3y-xy-2x2

p) 2n+24n+6

q) xx+2x+2

r) Bob simplifies x2+2x+2 to x2x (because he says “the 2s cancel”) and then to x. Explain where he went wrong.
______

s) Express n2+an+an as the sum of two fractions (and simplify as far as possible).
______

t) Do the same with n2-aan-a.
______

Decimal Manipulation

Without using a calculator:

a) 11.1×12=

b) 4.1×3.2=

c) 0.1×5.42=

d) 0.01×923.2=

e) 0.001×0.0037=

f) 4.51×13.2=

g) 6.12×0.21=

h) 938.2×0.0035=

i) 4.1×3.2=

j) 4.2÷0.1=

k) 423÷0.01=

l) 6÷0.125=

m) 9÷0.04=

n) 30÷0.4=

o) 40÷0.8=

p) 9÷0.375=

q) 36÷2.4=

r) 60÷7.5=

s) 6.4÷ 1.6

t) 7.5÷ 0.15

u) 0.27÷ 0.009

v) 4.2÷ 0.00014

w) 48÷ 0.06

x) 9.9÷ 0.11

y) 630÷ 0.09

For the following questions, you will need to use long division. Calculate to an appropriate number of decimal places.

a) 99.4÷ 71

b) 3.3÷ 22

c) 40.08÷ 2.4

d) 0.0255÷ 0.15

e) 0.3262÷ 0.14

f) 457÷ 13

g) 2.22÷ 1.7

h) 1.12÷ 0.03

i) 0.23÷ 1.1

j) 0.02÷ 0.11

Probability

Note that a pack of cards consists of 52 cards: 4 suits of 13 cards each (diamonds, clubs, spades, hearts). Each suit consists of 3 picture cards and 10 number cards.

1) By considering the matching outcomes and total outcomes, calculate the probability of the following (using correct notation!)

a. Rolling all 3s on 2 dice.

b. Rolling all 4s on 6 dice.

c. Rolling a total of 7 on two dice (you may want to draw a sample space table).

d. Rolling a total of 4 on 3 dice.

e. Pick a heart from a pack of cards.

f. Picking a picture card from a pack of cards.

g. Picking an even numbered heart.

2) If at each step I can move one square in 4 directions (N, S, W, E), the starting position is indicated by the dot at the centre and the destination indicated by the cross, find the probability that I end up in each of each of these positions after 2 steps:

3) Find the probability that:

a. When I pick a number randomly between 1 and 200, I don’t get a square number.

b. If the probability I pick Bob is 0.1 and the probability I pick Jim is 0.35, find the probability I pick neither.

c. If the probability I pick Alice and Bob is the same, and the probability I pick Cedric is three times that of Alice, find the probability I don’t pick Alice (presuming there’s no other people to pick from).

4) By drawing a sample space table or otherwise, find the probability that:

a. On a four-sided spinner (numbered 1 to 4) and a five-sided spinner (numbered 1 to 5), I get a 1 on both spinners.

b. I get an even number on both spinners.

c. I get a sum of 5 on both spinners.

5) I throw an unfair coin 200 times. The probability I throw a Heads is 0.3. How many tails do I expect to see?

6) Bill claims that the theoretical probability of flipping a heads on a coin is 0.4. When I throw the coin 300 times, I see a Heads 126 times.

a. What is the relative frequency/experimental probability of getting a Heads?

b. Comment on Bill’s claim.

Straight Line Graphs

1) In the equation y=2x-1, what is:

a. The gradient?

b. The y-intercept?

2) In the equation y=3-7x, what is:

a. The gradient?

b. The y-intercept?

3) For the line with equation y=3x+2, what is the coordinate of the y-intercept?

4) If y=5-2x, give the coordinate of the point on the line when:

a. x=1

b. x=-2

5) Find the equation of the line that has gradient 3 and goes through the point (0,-5).

6) Identify the equations of the following lines:

7) Find the gradient of the line that goes through the following two points:

a. 0,0 and 2,6.

b. 0,2 and 3,5.

c. -1,-3 and 3,5.

d. -2,7 and 2,-5.

e. -4,0 and 2,-3.

8) Find the equation of the line that goes through the following two points:

a. -1,2 and 2,5.

b. -1,-4 and 2,2.

c. -6,4 and 3,1.

Ratio and Proportion

1) The ratio of red sweets to green sweets to blue sweets in a bag is 2 : 3 : 5. There are 12 green sweets. How many blue sweets are there?

2) The ratio of cost of a PS3 game and an XBox360 game is 6 : 5. The Xbox game costs £150. How much does the PS3 game cost?

3) The ratio of boys to girls in a class is 3:5. There are 32 pupils in the class. How many girls are there?

4) The ratio of blue to red balls in a bag is 3:4. There are 28 balls in total. How many red balls are there?

5) Concrete consists of 1 part cement and 3 parts water. How much cement is needed to make 20 tonnes of concrete?

6) A fish tank is filled with 15 Clownfish and 17 Pufferfish. What is the ratio of Clownfish to Pufferfish?

7) The ratio of three internal angles of a triangle is 1:3:5. What is the smallest angle?

8) I have a full fish tank consisting of just red and yellow fish in the ratio 2 to 1. A plague wipes out 14 of each type of fish in my tank. I replenish my tank with just yellow fish such that the tank is full again. What is the ratio of red to yellow fish now?

Areas of Parallelograms and Trapeziums

1) A parallelogram has ___ pair(s) of parallel sides.

2) A trapezium has ___ pair(s) of parallel sides.

3) Find the area of the following:

4) What is the perpendicular distance between lines AB and CD in this diagram? (Hint: can you think of two ways in which the area of the parallelogram could be calculated?)

5) Find the area of the shaded region.

Formulae

1) Given x=2 and y=3, evaluate 2x-3y.

2) Given x=-1 and z=3, evaluate 5z-4x

3) Given that x=-1 and y=3, evaluate x2+y2-x.

4) Given that x=-2, evaluate x3+x2+x

5) Given that x=-2, evaluate x3-x2-x

6) Given that h=3.1 and x=-4.4, evaluate πx2-3hx

7) Find the value of x when y=4 and x=3yy-2y2

Significant Figures and Approximation

1) What is 0.00198452 to:

4sf?
3sf?
2sf?
1sf?

2) What is 14049 to 3sf?

3) What is 10999 to 3sf?

4) Without using a calculator, give an approximate value to:

8.1×3.90.52
0.34×12.11.95
5.14×8.940.19

Quadratic Graphs

1) What is the name of a line corresponding to a quadratic equation?

2) Given that y=x2-x-6 complete the following table:

x / -3 / -2 / -1 / 0 / 1 / 2 / 3 / 4
y

Hence draw suitable axis and plot the graph.

3) Given that y=9-x2, complete the following table:

x / -3 / -2 / -1 / 0 / 1 / 2 / 3
y

Hence draw suitable axis and plot the graph.

4) y = 4-4x-x2. Find y when x=-3.

5) Match the graphs to the equations, and give a reason.

Equation A: y=x2+4x+7

Equation B: y=x2

Equation C: y=-2x2-6x+8

Laws of Indices

1) Simplify the following:

a. 2923

b. 34×32

c. 96×9-3

d. 3×35

e. 676-2

f. 10-110-3

g. 572

h. 4-3-2

i. 393×36

j. 2-1

k. 20

l. 3-3

2) Simplify the following:

a. 162-3

b. 2736

3) What is the surface area of 6 cubes each of side 66? (Leave your answer in index form)

4) What is the volume of 5 cubes each of side 55?

5) Simplify
7377742×75

6) Solve 92x+1=27x-1

Changing the Subject of the Formula

Change the subject to the bracketed letter.

1) a=b-cd (b)

2) a=b-cd (c)

3) 2a=c+2e (e)

4) a-2b=3-2πd (d)

5) πb=2(c-d) (c)

6) 2e=3(x-d) (d)

7) a=xe (x)

8) a=xe (e)

9) a+1=xe (x)

10) a+1=xe (e)

11) x=yz+1 (y)

12) x=yz+1 (z)

13) x=2(a-bx) (b)

14) ya=5(7-qr) (r)

15) x2=e (x)

16) ax2+1=e (x)

17) ax-2=bc+2 (x)

18) D=ab-10x (x)

19) D=ab-10x (a)

20) D=ab-10x (b)

For these last few, you need to know how to expand two brackets each with multiple terms:

21) xy+1=z-1w (w)

22) xy+1=ws+1 (y)

23) y-3x-z=zy+2 (x)

Factorising

Factorise the following expressions as fully as possible.

1) 2+2x

2) 9-6xy

3) x2-2x

4) xy2-2x2y

5) 2pq2r+4p2q

6) 15px3-10px2

7) 24pqr-18pr

8) 5x4y2+10x3y3+15x2y4

Expanding out brackets each with multiple terms

1) x+1x+2

2) x-3x+4

3) x+62

4) x+y2

5) 2x+1x-4

6) 2y-13y+2

7) 4x-3x+5

8) x+ay+b

9) 2x+12

10) 9x-22

11) Show that it is not in general true that x+y2=x2+y2

Bearings

Determine the bearing from A to B in each case. (In each case the vertical line points to North)

Prisms

Find the volume of the following prisms.

Solving Equations

Solve the following equations.

1) 9y-3=42

2) 4x-15=2x-7

3) 57-z=5-10(4-3z)

4) 10=9-z5

5) 8y – 3 = 6y + 7

6) 7x-3=10x+3

7) x = 2-x

8) 2z= 9-z

9) 9t = 99 – 2t

10) x – 2(2-x) = 3(x-2) – x

11) 6 + 3(y-2) = 5(y+4)

12) 2(x+1) = 9 + x

13) x+43=2z-12

14) z-32=26-2z

15) 3-y5=3y+23

Mass and Density

1) A piece of copper has a mass of 30kg and a volume of 0.5m3. Determine the density of copper.

2) A liquid has a density of 6.5g/cm3. The volume of liquid in a glass is 50cm3. Determine the mass of the liquid.

Standard Form

1) Put the following in Standard Form:

30,000
290
0.4
0.071
3,100,000
52
10
0.000803

2) Express the following as normal numbers:

5.1×103
7.31×104
3×101
7×10-1
9.1×10-4
4.01×10-3
6×100

3) Determine the following results:

3×103×2×102
5×106×3×103
7×10-3×2×107
(9×109)×9×10-3
8×1092×103
4×1088×104
2×1078×10-4

4) Which is bigger, 4×102 or 2×104?

5) What is 6×103-3×103 in Standard Form?

Transformations

1) Reflect this shape in the line y =-x

2) Reflect this shape in the line x=-1

3) Write the equation of the line of reflection.

Equation: ______

5) A point (3,5) is translated to (1,6). What was the translation vector?

6) A point (-3,5) is translated by the transformation vector -2-3. What is the resulting point?

7) A point (-2, 3) is translated by the transformation vector -34. What is the resulting point?

8) A point (-2,5) is translated to (6,1). What was the translation vector?

9) Translate the following shape by the translation vector 3-4.

10) Translate the following shape by the translation vector -2-3.

11) What was the translation vector?

12) Rotate this shape 180° about the point (-1, 1).

13) Rotate this shape 90° anticlockwise about the point (1, 1).

14) Rotate this shape 90° clockwise about the point (-2, 2).

15) Describe the rotation.

______

16) Describe the rotation.

______

17) Describe the rotation.

18) Describe the following using a single transformation.

Polygons

1) Identify the missing angles.

2) How many sides does a regular polygon have if the exterior angle is 36°?

How many sides does a regular polygon have if the interior angle is 162°?