Mathematics Foundation and Higher Flashcards

A car travels 150 miles in 2.5 hours. What is its average speed?

Answer: 60 mph

Average speed = distance ÷ time = 150 ÷ 2.5 = 60 mph. The speed-distance-time triangle is a key tool for these calculations.

Factorise the expression x² + 7x + 12.

Answer: (x + 3)(x + 4)

Find two numbers that multiply to 12 and add to 7. Those numbers are 3 and 4 (3 × 4 = 12, 3 + 4 = 7). So x² + 7x + 12 = (x + 3)(x + 4).

Convert 0.375 to a fraction in its simplest form.

Answer: 3/8

0.375 = 375/1000. Divide numerator and denominator by 125: 375 ÷ 125 = 3, 1000 ÷ 125 = 8. So 0.375 = 3/8.

The exterior angle of a regular polygon is 40°. How many sides does the polygon have?

Answer: 9

The sum of exterior angles of any polygon is 360°. For a regular polygon, each exterior angle is equal, so the number of sides = 360° ÷ 40° = 9.

If y is directly proportional to x and y = 15 when x = 3, what is y when x = 7?

Answer: 35

y = kx where k is the constant of proportionality. When y = 15 and x = 3: 15 = 3k, so k = 5. When x = 7: y = 5 × 7 = 35.

What is the gradient of the line passing through the points (2, 3) and (6, 11)?

Answer: 2

Gradient = (y₂ - y₁) ÷ (x₂ - x₁) = (11 - 3) ÷ (6 - 2) = 8 ÷ 4 = 2. The gradient measures the steepness of the line.