Stage 8 - Q1 - 2 marks
Solve.
Hint
Form the relationship first, then simplify it before solving.
Stage 8 - Q2 - 2 marks
Solve.
Hint
Form the relationship first, then simplify it before solving.
Stage 8 - Q3 - 3 marks
Solve.
Hint
Form the relationship first, then simplify it before solving.
Stage 8 - Q4 - 3 marks
Solve.
Hint
Form the relationship first, then simplify it before solving.
Stage 8 - Q5 - 4 marks
A rectangle has length \(x+1\) cm and width \(10x\) cm. Its perimeter is 310 cm. Find x and both side lengths.
Hint
Form the relationship first, then simplify it before solving.
Stage 8 - Q6 - 4 marks
A rectangle has length \(x+3\) cm and width \(3x\) cm. Its perimeter is 70 cm. Find x and both side lengths.
Hint
Form the relationship first, then simplify it before solving.
Stage 8 - Q7 - 5 marks
Solve \(6(2x-3)=4(x+5)\) and verify the result.
Hint
The answer need not be an integer.
Stage 8 - Q8 - 5 marks
For what value of k does \(4(x+3)=4x+k\) hold for every x? What happens for any other k?
Hint
Expand and remove the matching variable terms.
Stage 8 - Q9 - 5 marks
Two equal sides of an isosceles triangle are \(3x+1\) cm and \(5x-7\) cm. The third side is \(x+2\) cm. Find the perimeter and check that a triangle is possible.
Hint
Use the equal-side condition before calculating the perimeter.
Stage 8 - Q10 - 5 marks
A rectangle has length \(3x+2\) cm and width \(x-1\) cm. Its perimeter equals that of a square with side \(2x+3\) cm. Is there any value of x that makes this possible? Explain.
Hint
Simplify both perimeters before trying to solve for x.