Question 1Aim for about 60 seconds
Solve for x.
7x + 20 = 69
Show the worked answer
Answer: B, 7
How to work it out
- Take 20 from both sides: 7x = 49.
- Divide both sides by 7: x = 7.
Algebra: 11 Plus maths practice
Solving equations, substitution and “think of a number”.
OftenIn many papers, especially GL AssessmentAbout 60 seconds a question in the test
The big idea
Algebra uses letters for unknown numbers. To solve an equation, do the same thing to both sides until the letter is on its own.
Work backwards through “think of a number” problems using inverse operations: undo adding by subtracting, undo multiplying by dividing.
Tips that save marks
- 3n means 3 × n.
- Substitute your answer back in to check it.
- Undo operations in reverse order.
A worked example
Solve 4x + 7 = 31.
- Subtract 7: 4x = 24.
- Divide by 4: x = 6.
- Check: 4 × 6 + 7 = 31 ✓
Now try five
Try each one before you look at the answer: answering from memory is what makes it stick. Tap an option to check it. Most children get three or four right at first; five out of five means move on to the next topic.
Question 2Aim for about 60 seconds
11 goes into this machine. What comes out?
Show the worked answer
Answer: D, 48
How to work it out
Follow the steps in order: 11 × 4 = 44, then + 4 = 48.
Why the other options are wrong
- A (60): This adds 4 first and multiplies after. Follow the machine from left to right.
- B (19): This adds every number instead of multiplying first.
- C (40): This subtracts 4 instead of adding it.
- E (44): This stops after the first step: it still needs + 4.
Question 3Aim for about 60 seconds
I think of a number, multiply it by 4 and add 5. The answer is 61. What was my number?
Show the worked answer
Answer: C, 14
How to work it out
Work backwards with the inverse steps: 61 − 5 = 56, then 56 ÷ 4 = 14.
Question 4Aim for about 60 seconds
The perimeter of a rectangle is P = 2 × (l + w), where l is the length and w is the width. What is the perimeter when l = 10 cm and w = 5 cm?
Show the worked answer
Answer: C, 30 cm
How to work it out
- Brackets first: 10 + 5 = 15.
- Then × 2: 30 cm.
Why the other options are wrong
- A (15 cm): This forgets to multiply by 2: a rectangle has two lengths and two widths.
- B (50 cm): This is the area, not the perimeter.
- D (100 cm): This multiplies the length and width; the formula adds them.
- E (25 cm): This doubles the length only; the brackets mean both are doubled.
Question 5Aim for about 60 seconds
I think of a number, multiply it by 5 and add 16. The answer is 116. What was my number?
Show the worked answer
Answer: E, 20
How to work it out
Work backwards with the inverse steps: 116 − 16 = 100, then 100 ÷ 5 = 20.
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