(a) Write in figures six million three thousand and seventy six.
(b) (i) Work out the value of p when p = –0.6 ÷ 1.6.
(ii) Work out the value of q when q = –0.6 – 1.6.
(iii) Use one of the symbols >, <, ≥, ≤, = to complete this statement.
(c) Mount Robson in Canada has a height of 3950 metres, correct to the nearest 10 metres.
Complete the following statement about the height, h m, of Mount Robson.
(d) Calculate \(2\frac{1}{12}\div 1\frac{1}{4}.\)
Give your answer as a decimal, correct to 4 significant figures.
(e) (i) Write down the value of 80.
(ii) Work out 5–3.
Write your answer as a fraction.
(iii) Simplify the expression.
8x5 × 3x4
▶️ Answer/Explanation
(a) 6,003,076 – Six million = 6,000,000; three thousand = 3,000; seventy-six = 76.
(b)(i) –0.375 – \( p = \frac{-0.6}{1.6} = -0.375 \).
(b)(ii) –2.2 – \( q = -0.6 – 1.6 = -2.2 \).
(b)(iii) > – Since –0.375 > –2.2.
(c) 3945 ≤ h < 3955 – Nearest 10m means height rounds to 3950m, so range is 3945m to 3955m.
(d) 1.667 – Convert to improper fractions: \( \frac{25}{12} ÷ \frac{5}{4} = \frac{25}{12} × \frac{4}{5} = \frac{100}{60} ≈ 1.6667 \) (4 s.f.).
(e)(i) 1 – Any non-zero number to the power of 0 is 1.
(e)(ii) \(\frac{1}{125}\) – \( 5^{-3} = \frac{1}{5^3} = \frac{1}{125} \).
(e)(iii) 24x9 – Multiply coefficients: \(8 × 3 = 24\); add exponents: \(x^{5+4} = x^9\).
(a)
Write down an expression for the area of this rectangle.
Give your answer in its simplest form.
(b) In this part, all measurements are in centimetres.
The perimeter of the triangle is 526 cm.
Find the value of x.
▶️ Answer/Explanation
(a) Ans: 6y²
Area of rectangle = length × width
Given dimensions: 3y (length) and 2y (width)
Area = 3y × 2y = 6y²
(b) Ans: x = 64.5
Perimeter equation:
(3x – 10) + (x + 70) + (4x – 50) = 526
Combine like terms:
8x + 10 = 526
Solve for x:
8x = 516
x = 64.5 cm