Daily Practice · Higher Plus
July 1989 5-a-day
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The batch download puts all 5 tiers' July 1989 sheets in a single PDF, each tier behind its own divider page - 155 sheets in one file.
Every sheet in July 1989
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st July 1989A cuboid measures 4 cm by 10 cm by 13 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 2nd July 1989A bag holds 4 red, 5 blue and 2 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 3rd July 1989On a histogram, a 5-wide bar and a 10-wide bar have the same frequency density of 2. How many more values are in the wider class?
- 4th July 1989Expand and simplify (2 + sqrt(5))(2 - sqrt(5)).
- 5th July 1989Solve 16x^2 + 32x + 15 = 0.
- 6th July 1989A train slows steadily from 20 m/s to rest in 4 seconds. Work out its deceleration.
- 7th July 1989The point (9, 40) lies on the circle x^2 + y^2 = 1681. Work out the gradient of the tangent to the circle at that point.
- 8th July 1989A bag holds 8 counters, r of them red. Two are taken without replacement and P(both red) = 3/28. Work out r.
- 9th July 1989A histogram has two bars: one 10 units wide with frequency density 1.5, one 25 units wide with density 0.6. How many values in total?
- 10th July 1989A block has mass 610 g (to the nearest 10 g) and volume 3 cm^3 (to the nearest cm^3). Work out the upper bound of its density, to 2 decimal places.
- 11th July 1989f(x) = 5x + 3. Work out the inverse function f^-1(x).
- 12th July 1989y is inversely proportional to x^2. When x = 4, y = 9. Work out y when x = 3.
- 13th July 1989In a circle theorem proof, a step uses the fact that a triangle is drawn from the ends of a diameter to a point on the circle. State the reason being quoted.
- 14th July 1989The probability of winning a game is 1/5. A player expects 5 wins. How many games did they play?
- 15th July 1989On a histogram, a 4-wide bar and a 8-wide bar have the same frequency density of 2. How many more values are in the wider class?
- 16th July 1989x = 179 and y = 26, each correct to the nearest whole number. Work out the upper bound of x - y.
- 17th July 1989Solve x^2 + y^2 = 100 and y = x - 2 simultaneously.
- 18th July 1989y is directly proportional to x^3. When x = 4, y = 192. Work out y when x = 3.
- 19th July 1989In a vector proof you find that vector PQ = 3a + 6b and vector RS = 6a + 12b. What does this show about PQ and RS?
- 20th July 1989A bag holds 4 red and n blue counters. The probability of taking a red is 1/2. Work out n.
- 21st July 1989A histogram has two bars: one 20 units wide with frequency density 1.2, one 5 units wide with density 3.5. How many values in total?
- 22nd July 1989A car covers 530 m (to the nearest 10 m) in 2 s (to the nearest second). Work out the lower bound of its speed, to 2 decimal places.
- 23rd July 1989Use the iteration x(n+1) = cube root of (12x(n) + 1) with x(0) = 4. Work out x(1) to 3 decimal places.
- 24th July 1989y is directly proportional to sqrt(x). When x = 25, y = 15. Work out y when x = 4.
- 25th July 1989A cuboid measures 13 cm by 14 cm by 11 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 26th July 1989A bag holds 7 red and 6 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
- 27th July 1989On a histogram, a 10-wide bar and a 30-wide bar have the same frequency density of 2.5. How many more values are in the wider class?
- 28th July 1989Rationalise the denominator of 21/sqrt(3), giving your answer in its simplest form.
- 29th July 1989Work out the nth term of the quadratic sequence 0, 3, 8, 15, ...
- 30th July 1989A train slows steadily from 14 m/s to rest in 10 seconds. Work out its deceleration.
- 31st July 1989A cuboid measures 9 cm by 4 cm by 14 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.