Pack A — Fluency

Mathematics

Year 7 · 7.3 Introduction to Algebra

Pack A · Fluency

Name: _________________________________

Date: _________________ Class: ___________

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

BronzeQuestions 1–11

1.
If $a = 4$ , find a value of $b$ so that $3a + b = 15$ . Justify your answer.
2.
Which of these is the correct algebraic convention: $n3$ or $3n$ ? Explain why the other form is wrong.
3.
Write $ $8x$ 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 $x = 8$ . Solve it to check.
5.
A number of chairs $n$ is arranged in 4 equal rows. Write an equation for this and solve it to find $n$ .
6.
Expand $3(x + 4)$ and show that your answer gives the same value as the original expression when $x = 2$ .
7.
Solve $2x + 5 = 17$ and check your answer by substituting back.
8.
Write two different expressions that both describe "a number $n$ multiplied by 4, then subtract 3". Explain why they are the same.
9.
Decide: are $9y$ and $4y$ like terms? Simplify $9y - 4y$ and justify your step.
10.
In the expression $7x + 3$ , identify the coefficient of $x$ and the constant. Explain what each part tells you about the expression.
11.
Little puzzle: what number $a$ makes $a \times 5 = 0$ ? How did you know?

SilverQuestions 12–22

12.
Find the value of $2a + 3b$ when $a = 3$ and $b = 4$ .
13.
Simplify: $5x + 3y + 2x - 1y$ .
14.
Expand and simplify: $4(x + 3) + 5$ .
15.
Solve: $4x - 3 = 21$ .
16.
Tickets to a show cost $\pounds {p}$ each. 5 friends buy tickets. Write an expression for the total cost, then find the cost when $p = 8$ .
17.
Find the value of $3x^2$ when $x = 4$ .
18.
Simplify: $6a + 5b + 2a - 3b$ .
19.
A rectangle has length $(x + 3)$ cm and width $4$ cm. Write a simplified expression for its perimeter.
20.
Expand the bracket: $4(2x - 5)$ .
21.
Solve: $\dfrac{x}{{a}} + 4 = 9$ .
22.
Another little puzzle: what number $a$ makes $3(4 - a) = 0$ ? Try to spot the answer without doing lots of working.

GoldQuestions 23–32

23.
Simplify: $3x + 5x - 2x$ .
24.
Find the value of $3a^2 + 2a$ when $a = -2$ .
25.
Expand and simplify: $3(x + 2) + 2(x + 5)$ .
26.
Solve: $5x + 12 = 2$ .
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 3 bags of apples and 4 bags of oranges.
28.
Work out $4a - 3b$ when $a = -3$ and $b = 2$ .
29.
Solve: $5x + 3 = 2x + 15$ .
30.
A rectangle has length $(2x + 3)$ cm and width $(x + 5)$ cm. Its perimeter is 40 cm. Find $x$ .
31.
Expand and simplify: $3(2x - 4) - 5x$ .
32.
If $n = 2^2 \times 5$ , find the value of $3n - 7$ .

PlatinumQuestions 33–42

33.
I think of a number. I double it, then subtract 7. The result is -3. Find the number.
34.
Three consecutive integers have a sum of 48. Find the three integers and write an equation to show your method.
35.
Solve: $\dfrac{{a}x + 6}{{c}} = 9$ .
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 $\pounds 12$ plus $\pounds 3$ 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 $\pounds 33$ .
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: $x + y = 14$ and $x - y = 4$ . Find $x$ and $y$ .
40.
The perimeter of a triangle is $37$ cm. One side is $(2x + 3)$ cm, a second side is $(3x - 1)$ cm, and the third side is $10$ cm. Find $x$ and the length of each side.
41.
Explain why $5(x + 3)$ and $5x + 15$ are equal. What must 15 equal? Now expand $4(x - 2)$ and simplify $4(x - 2) + 6x$ .
42.
A number machine applies the rule " $\times 3$ , then $- 8$ ". An input gives an output of $7$ . Find the input. Then find the input that gives an output equal to the original input.