Stage 8 - Q1 - 2 marks
Solve.
Hint
Choose one operation that makes the equation simpler, and apply it to both sides.
Stage 8 - Q2 - 2 marks
Solve.
Hint
Choose one operation that makes the equation simpler, and apply it to both sides.
Stage 8 - Q3 - 3 marks
Solve.
Hint
Choose one operation that makes the equation simpler, and apply it to both sides.
Stage 8 - Q4 - 3 marks
Solve.
Hint
Choose one operation that makes the equation simpler, and apply it to both sides.
Stage 8 - Q5 - 4 marks
A number is multiplied by 11, then 17 is added. The result is 237. Form an equation and find the number.
Hint
Choose one operation that makes the equation simpler, and apply it to both sides.
Stage 8 - Q6 - 4 marks
A number is multiplied by 11, then 2 is added. The result is 90. Form an equation and find the number.
Hint
Choose one operation that makes the equation simpler, and apply it to both sides.
Stage 8 - Q7 - 5 marks
Solve \(5x-8=2x+13\), then explain why subtracting \(2x\) from both sides is a useful first step.
Hint
Choose a subtraction that removes one variable term.
Stage 8 - Q8 - 5 marks
Does \(3x+4=3x-2\) have a solution? Explain what the simplified equation tells you.
Hint
Try collecting the x terms and inspect what remains.
Stage 8 - Q9 - 5 marks
Three consecutive integers have sum 96. Form an equation and find them. Explain why the middle integer equals their mean.
Hint
Represent all three integers using only one unknown.
Stage 8 - Q10 - 5 marks
A two-digit positive integer has digit sum 11. Reversing its digits produces a number 27 greater. Find the original number and show that it is the only possibility.
Hint
Use place value to write each number in terms of one digit.