Pack B — Fluency

Mathematics

Year 7 · 7.3 Introduction to Algebra

Pack B · Fluency

Name: _________________________________

Date: _________________ Class: ___________

Answer all questions. Show your working. Questions are grouped by challenge level.

BronzeQuestions 1–11

1.
If $a = 6$ , find a value of $b$ so that $3a + b = 21$ . Justify your answer.
2.
Which of these is the correct algebraic convention: $n \times n$ or $n^2$ ? Explain why the other form is wrong.
3.
Write $ $11x$ in two different ways as a sum of like terms. Show each is equivalent to the original.
4.
Make up an equation whose solution is $x = 7$ . Solve it to check.
5.
A number of chairs $n$ is arranged in 5 equal rows. Write an equation for this and solve it to find $n$ .
6.
Expand $5(x + 2)$ and show that your answer gives the same value as the original expression when $x = 3$ .
7.
Solve $3x + 4 = 19$ and check your answer by substituting back.
8.
Write two different expressions that both describe "a number $n$ multiplied by 6, then subtract 5". Explain why they are the same.
9.
Decide: are $8y$ and $3y$ like terms? Simplify $8y - 3y$ and justify your step.
10.
In the expression $4x + 9$ , identify the coefficient of $x$ and the constant. Explain what each part tells you about the expression.
11.
Little puzzle: what number $a$ makes $a \times 7 = 0$ ? How did you know?

SilverQuestions 12–22

12.
Find the value of $2a + 3b$ when $a = 5$ and $b = 2$ .
13.
Simplify: $7x + 4y + 3x - 2y$ .
14.
Expand and simplify: $3(x + 5) + 7$ .
15.
Solve: $5x - 2 = 23$ .
16.
Tickets to a show cost $\pounds {p}$ each. 7 friends buy tickets. Write an expression for the total cost, then find the cost when $p = 6$ .
17.
Find the value of $2x^2$ when $x = 5$ .
18.
Simplify: $8a + 7b + 1a - 4b$ .
19.
A rectangle has length $(x + 5)$ cm and width $6$ cm. Write a simplified expression for its perimeter.
20.
Expand the bracket: $3(4x - 7)$ .
21.
Solve: $\dfrac{x}{{a}} + 3 = 8$ .
22.
Another little puzzle: what number $a$ makes $5(2 - a) = 0$ ? Try to spot the answer without doing lots of working.

GoldQuestions 23–32

23.
Simplify: $6x + 4x - 3x$ .
24.
Find the value of $3a^2 + 2a$ when $a = -3$ .
25.
Expand and simplify: $4(x + 3) + 3(x + 2)$ .
26.
Solve: $5x + 9 = -1$ .
27.
A bag of apples costs ${p}p$ pence and a bag of oranges costs ${q}p$ pence. Write and simplify an expression for the total cost of 5 bags of apples and 2 bags of oranges.
28.
Work out $4a - 3b$ when $a = 2$ and $b = -5$ .
29.
Solve: $6x + 2 = 2x + 14$ .
30.
A rectangle has length $(2x + 2)$ cm and width $(x + 4)$ cm. Its perimeter is 36 cm. Find $x$ .
31.
Expand and simplify: $4(3x - 2) - 6x$ .
32.
If $n = 2^2 \times 3$ , find the value of $3n - 4$ .

PlatinumQuestions 33–42

33.
I think of a number. I double it, then subtract 5. The result is -9. Find the number.
34.
Three consecutive integers have a sum of 63. Find the three integers and write an equation to show your method.
35.
Solve: $\dfrac{{a}x + 4}{{c}} = 6$ .
36.
The expression $5n - 3$ is evaluated for two consecutive negative integers. Show that the difference between the two results is always 5, whatever negative integers you choose.
37.
A mobile phone plan charges a fixed monthly fee of $\pounds 15$ plus $\pounds 4$ per GB of data used. Write a formula for the monthly cost $C$ in terms of $g$ (GB used). Use it to find how many GB were used if the bill was $\pounds 51$ .
38.
Alice thinks of a prime number $p$ . She computes $p^2 - p$ . Show algebraically that the result is always even. Verify with $p = 7$ .
39.
Two numbers, $x$ and $y$ , satisfy: $x + y = 20$ and $x - y = 6$ . Find $x$ and $y$ .
40.
The perimeter of a triangle is $46$ cm. One side is $(3x + 2)$ cm, a second side is $(2x - 3)$ cm, and the third side is $7$ cm. Find $x$ and the length of each side.
41.
Explain why $6(x + 4)$ and $6x + 24$ are equal. What must 24 equal? Now expand $3(x - 5)$ and simplify $3(x - 5) + 7x$ .
42.
A number machine applies the rule " $\times 4$ , then $- 10$ ". An input gives an output of $6$ . Find the input. Then find the input that gives an output equal to the original input.