Robinson Tuition20 mixed questions from 8 Year 9 topics, 54 marks. It covers representing data to area and perimeter, the second third of the year in the order schools usually teach it.
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A bag contains 4 green counters, 7 yellow counters and 9 white counters.
A counter is taken from the bag at random.
Find the probability that the counter is not green.
Total counters
| 4 + 7 + 9 | = | 20 | ||
| Not green | ||||
| 7 + 9 | = | 16 | ||
| P(not green) | = | 1620 | ||
| ÷4 | P(not green) | = | 45 | ÷4 |
45
Priya thinks of a number.
She multiplies the number by 4 and then subtracts 9.
Her answer is 35.
Work out the number Priya thought of.
Let the number be n
| 4n - 9 | = | 35 | ||
| +9 | 4n | = | 44 | +9 |
| ÷4 | n | = | 11 | ÷4 |
Check
4 × 11 - 9 → 35
11
a)
| 5 | ≤ | 3x - 4 < 14 |
| +4 to all three parts | ||
| 9 | ≤ | 3x < 18 |
| ÷3 all three parts | ||
| 3 | ≤ | x < 6 |
3 ≤ x < 6
b)
Filled circle at 3, open circle at 6
Joined by a line
Here are the first four terms of a sequence.
14 11 8 5
a)
14 → 11 → 8 → 5: down 3 each time
| 5 - 3 | = | 2 |
| 2 - 3 | = | -1 |
2 and -1
b)
Subtract 3
A bistro menu has 5 starters, 8 main courses and 4 desserts.
Callum chooses one starter, one main course and one dessert.
Work out the number of different three-course meals Callum can choose.
Multiply the choices at each stage
starters × mains × desserts
| 5 × 8 | = | 40 |
| 40 × 4 | = | 160 |
160
The number line shows an inequality.
a)
Open circle, so not included
Arrow right, so greater than
x > -2
b)
-2 is not included
-1
a)
| t8 ÷ t3 | = | t8 - 3 |
| = | t5 |
t5
b)
| (k4)5 | = | k4 × 5 |
| = | k20 |
k20
c)
| 12 ÷ 4 | = | 3 |
| x6 ÷ x2 | = | x4 |
| y3 ÷ y1 | = | y2 |
3x4y2
a)
| C | = | 2πr | ||
| ÷2π | C2π | = | r | ÷2π |
r = C2π
b)
| P | = | 2(a + b) | ||
| ÷2 | P2 | = | a + b | ÷2 |
| -a | P2 - a | = | b | -a |
b = P2 - a
c)
| y | = | x + 43 | ||
| ×3 | 3y | = | x + 4 | ×3 |
| -4 | 3y - 4 | = | x | -4 |
x = 3y - 4
40 students each chose one sport. 15 chose football and 6 chose tennis. Ellie is going to draw a pie chart of the results.
Angle for one student
| 360° ÷ 40 | = | 9° |
| a) | ||
| Football | = | 15 × 9° |
| Football | = | 135° |
135°
b)
| Tennis | = | 6 × 9° |
| Tennis | = | 54° |
54°
The diagram shows a trapezium.
a)
Area = (a + b)2 × h
| Area | = | 9 + 122 × 4 |
| Area | = | 10.5 × 4 |
| Area | = | 42 cm² |
42 cm²
b)
Add all four sides
| Perimeter | = | 12 + 5 + 9 + 4 |
| Perimeter | = | 30 cm |
30 cm
a)
n = 1: 20 - 3 × 1 = 17
n = 2: 20 - 3 × 2 = 14
n = 3: 20 - 3 × 3 = 11
n = 10: 20 - 3 × 10 = -10
17, 14, 11 and -10
b)
n = 1: 12 + 2 = 3
n = 2: 22 + 2 = 6
n = 3: 32 + 2 = 11
3, 6, 11
Make k the subject of the formula
m = k5 - 2
| m | = | k5 - 2 | ||
| +2 | m + 2 | = | k5 | +2 |
| ×5 | 5(m + 2) | = | k | ×5 |
k = 5(m + 2)
On the number line, show the inequality −1 < x ≤ 3
< means not included: open circle
Open circle at -1
≤ means included: filled circle
Filled circle at 3
Join them with a line
Open circle at -1, filled circle at 3, joined
Choose the most suitable diagram for each set of data from this list.
pie chart scatter graph time series graph frequency polygon
a) values over time
time series graph
b) two measurements for each pupil
scatter graph
c) parts of a whole
pie chart
d) grouped data
frequency polygon
a)
| s | = | 3 × 4 + 12 × 2.5 × 42 |
| s | = | 12 + 12 × 2.5 × 16 |
| s | = | 12 + 20 |
| s | = | 32 |
32 m
b)
| F | = | 9 × 255 + 32 |
| F | = | 2255 + 32 |
| F | = | 45 + 32 |
| F | = | 77 |
77 °F
Expand and simplify (x + 2)(x + 3)(x + 4)
Expand the first two brackets
| (x + 2)(x + 3) | = | x2 + 3x + 2x + 6 |
| (x + 2)(x + 3) | = | x2 + 5x + 6 |
Multiply by the third bracket
(x2 + 5x + 6)(x + 4)
x3 + 4x2 + 5x2 + 20x + 6x + 24
Collect like terms
x3 + 9x2 + 26x + 24
a)
| 12 × w | = | 84 | ||
| ÷12 | w | = | 7 | ÷12 |
7 cm
b)
| 12 × 9 × h | = | 36 | ||
| 4.5h | = | 36 | ||
| ÷4.5 | h | = | 8 | ÷4.5 |
8 cm
A circle has radius 6 cm.
a)
| C | = | 2πr |
| C | = | 2 × π × 6 |
| C | = | 37.6991... |
Round to 1 dp
37.7 cm
b)
| A | = | πr2 |
| A | = | π × 62 |
| A | = | 113.0973... |
Round to 1 dp
113.1 cm2
a)
(i)
subtract 7
(ii)
divide by 4
(iii)
multiply by 3
b)
Work backwards, undo the last step first
| 29 - 8 | = | 21 |
| 21 ÷ 3 | = | 7 |
7
Ollie buys 4 cinema tickets and one large popcorn.
Each ticket costs £t. The popcorn costs £6.
He pays £38 altogether.
a) 4 tickets at £t plus £6
4t + 6 = 38
b)
| 4t + 6 | = | 38 | ||
| -6 | 4t | = | 32 | -6 |
| ÷4 | t | = | 8 | ÷4 |
£8
Answer the questions above and your score appears here.
Every question here is original and written by Robinson Tuition, drawn from the Year 9 topic worksheets. It follows the Key Stage 3 programme of study.