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.

Fractions c) 0.72 as a fraction in its simplest form: ______Give answers as mixed numbers where appropriate. d) 0.4 as a fraction in its simplest form: ______a) e) 1.125 as a fraction in its simplest form: b) ______

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

e) g) Use long division for find the exact value of . f) ______g) h) Use long division to find to 3dp. ______h) i) Find to 3dp. i) ______j) j) Find to 5dp. k) ______Pythagoras Theorem l) Find the sides labelled with a variable. When m) appropriate, give your answers in both decimal n) and surd form.

o) The following are more challenging: p) Algebraic Simplification q) Simplify the following Converting between decimals and fractions a) a) 1.62 as a percentage: ______b) b) 68% as a decimal: c) ______www.drfrostmaths.com d) t) Do the same with . ______e)

f) Decimal Manipulation

g) Without using a calculator:

a) h) b)

c) i) d)

j) e)

f) k) g)

l) h)

i) m) j) n) k)

o) l) p)

q) m)

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

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

www.drfrostmaths.com o) x)

p) y)

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

www.drfrostmaths.com 2) If at each step I can move one square in 4 directions (N, S, W, E), the starting position is g) 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:

h) 3) Find the probability that:

a. When I pick a number randomly between 1 and 200, I don’t get a square number. i) 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 j) is the same, and the probability I pick Cedric is three times that of Alice, find the probability I don’t pick Alice Probability (presuming there’s no other people to pick from). Note that a pack of cards consists of 52 cards: 4 suits of 13 cards each (diamonds, clubs, spades, 4) By drawing a sample space table or hearts). Each suit consists of 3 picture cards and otherwise, find the probability that: 10 number cards. a. On a four-sided spinner (numbered 1 1) By considering the matching outcomes and to 4) and a five-sided spinner total outcomes, calculate the probability of (numbered 1 to 5), I get a 1 on both the following (using correct notation!) spinners.

a. Rolling all 3s on 2 dice. b. I get an even number on both spinners. b. Rolling all 4s on 6 dice. c. I get a sum of 5 on both spinners. c. Rolling a total of 7 on two dice (you may want to draw a sample space 5) I throw an unfair coin 200 times. The table). probability I throw a Heads is 0.3. How many tails do I expect to see? d. Rolling a total of 4 on 3 dice. 6) Bill claims that the theoretical probability of e. Pick a heart from a pack of cards. flipping a heads on a coin is 0.4. When I throw the coin 300 times, I see a Heads 126 f. Picking a picture card from a pack of times. cards. a. What is the relative g. Picking an even numbered heart. frequency/experimental probability of getting a Heads? www.drfrostmaths.com b. Comment on Bill’s claim. d. and .

e. and .

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

Straight Line Graphs a. and .

b. and .

1) In the equation , what is: c. and .

a. The gradient? Ratio and Proportion

b. The y-intercept? 1) The ratio of red sweets to green sweets to blue sweets in a bag is 2 : 3 : 5. There are 12 2) In the equation , what is: green sweets. How many blue sweets are there? a. The gradient? 2) The ratio of cost of a PS3 game and an b. The y-intercept? XBox360 game is 6 : 5. The Xbox game costs 3) For the line with equation , what is the £150. How much does the PS3 game cost? coordinate of the y-intercept? 3) The ratio of boys to girls in a class is 3:5. 4) If , give the coordinate of the point on the There are 32 pupils in the class. How many line when: girls are there?

a. 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?

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

5) Find the equation of the line that has 6) A fish tank is filled with Clownfish and gradient 3 and goes through the point . Pufferfish. What is the ratio of Clownfish to Pufferfish? 6) Identify the equations of the following lines: 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 7) Find the gradient of the line that goes and yellow fish in the ratio 2 to 1. A plague through the following two points: wipes out of each type of fish in my tank. I a. and . replenish my tank with just yellow fish such that the tank is full again. What is the ratio of b. and . red to yellow fish now?

c. and . www.drfrostmaths.com 7) Find the value of when and

Significant Figures and Approximation

1) What is 0.00198452 to:

a. 4sf?

b. 3sf?

c. 2sf?

Areas of Parallelograms and Trapeziums d. 1sf?

1) A parallelogram has ___ pair(s) of parallel 2) What is 14049 to 3sf? sides. 3) What is 10999 to 3sf? 2) A trapezium has ___ pair(s) of parallel sides. 4) Without using a calculator, give an 3) Find the area of the following: approximate value to:

4) What is the perpendicular distance between c. lines and 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 and , evaluate .

2) Given and , evaluate

3) Given that and , evaluate . Quadratic Graphs 4) Given that , evaluate 1) What is the name of a line corresponding to a 5) Given that , evaluate quadratic equation?

6) Given that and , evaluate 2) Given that complete the following table: www.drfrostmaths.com x -3 -2 -1 0 1 2 3 4 y Hence draw suitable axis and plot the graph. d.

3) Given that , complete the following table:

e. x -3 -2 -1 0 1 2 3 y Hence draw suitable axis and plot the graph.

4) . Find when . f. 5) Match the graphs to the equations, and give a reason.

Equation A: g. Equation B:

Equation C:

Laws of Indices i. 1) Simplify the following:

www.drfrostmaths.com 2) Simplify the following: 5) (c)

a. 6) (d)

7) (x)

8) (e) b. 9) (x)

10) (e) 3) What is the surface area of 6 cubes each 11) (y) of side ? (Leave your answer in index form) 12) (z)

4) What is the volume of 5 cubes each of 13) (b) side ? 14) (r) 5) Simplify 15) (x)

6) Solve 16) (x) 17) (x)

18) (x)

19) (a)

20) (b)

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

21) (w)

22) (y)

23) (x)

Changing the Subject of the Formula

Change the subject to the bracketed letter.

1) (b)

2) (c)

3) (e) Factorising 4) (d) www.drfrostmaths.com Factorise the following expressions as fully as Find the volume of the following prisms. possible.

1) Solving Equations 2) Solve the following equations. 3) 1) 4) 2) 5) 3) 6) 4)

7) 5) 8y – 3 = 6y + 7

8) 6) Expanding out brackets each with multiple terms 7) 1)

3) 8) 4)

5) 9) 9t = 99 – 2t 6) 10) x – 2(2-x) = 3(x-2) – x 7) 11) 6 + 3(y-2) = 5(y+4) 8) 12) 2(x+1) = 9 + x 9) 13) 10) 14) 11) Show that it is not in general true that 15) Bearings Mass and Density Determine the bearing from A to B in each case. (In each case the vertical line points to North) 1) A piece of copper has a mass of 30kg and a volume of 0.5m3. Determine the density of copper. Prisms www.drfrostmaths.com 2) A liquid has a density of 6.5g/cm3. The f. volume of liquid in a glass is 50cm3. Determine the mass of the liquid. g. Standard Form 4) Which is bigger, or ? 1) Put the following in Standard Form: 5) What is in Standard Form? a. 30,000

b. 290

c. 0.4

d. 0.071

e. 3,100,000

f. 52

g. 10

h. 0.000803 Transformations 2) Express the following as normal numbers: 1) Reflect this shape in the line a.

3) Determine the following results: 2) Reflect this shape in the line

www.drfrostmaths.com 3) Write the equation of the line of reflection. 10) Translate the following shape by the translation vector .

Equation: ______

11) What was the translation vector?

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 . What is the resulting point?

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

8) A point (-2,5) is translated to (6,1). What was the translation vector? 12) Rotate this shape 180° about the point (- 1, 1). 9) Translate the following shape by the translation vector . www.drfrostmaths.com 13) Rotate this shape 90° anticlockwise about the ______point (1, 1). 16) Describe the rotation.

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

17) Describe the rotation.

15) Describe the rotation.

www.drfrostmaths.com 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 ?

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