Daily Practice · Higher Plus
August 1990 5-a-day
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The batch download puts all 5 tiers' August 1990 sheets in a single PDF, each tier behind its own divider page - 155 sheets in one file.
Every sheet in August 1990
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st August 1990The point (5, 12) lies on the circle x^2 + y^2 = 169. Work out the gradient of the tangent to the circle at that point.
- 2nd August 1990A bag holds 11 counters, r of them red. Two are taken without replacement and P(both red) = 1/55. Work out r.
- 3rd August 1990On a histogram, a 5-wide bar and a 20-wide bar have the same frequency density of 3. How many more values are in the wider class?
- 4th August 1990A car covers 370 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.
- 5th August 1990Make x the subject of 8x + 7 = y(x + 7).
- 6th August 1990y is directly proportional to x^3. When x = 3, y = 135. Work out y when x = 4.
- 7th August 1990In a circle theorem proof, a step uses the fact that opposite angles of a cyclic quadrilateral are being proved. State the reason being quoted.
- 8th August 1990The probability of winning a game is 2/5. A player expects 28 wins. How many games did they play?
- 9th August 1990A histogram has two bars: one 10 units wide with frequency density 1.5, one 10 units wide with density 1.4. How many values in total?
- 10th August 1990Rationalise the denominator of 9/sqrt(3), giving your answer in its simplest form.
- 11th August 1990Write 2/(x - 3) + 6/(x + 2) as a single fraction.
- 12th August 1990y is directly proportional to sqrt(x). When x = 25, y = 40. Work out y when x = 36.
- 13th August 1990In a vector proof you find that vector PQ = 2a + 2b and vector RS = 6a + 6b. What does this show about PQ and RS?
- 14th August 1990A bag holds 7 red and n blue counters. The probability of taking a red is 7/12. Work out n.
- 15th August 1990On a histogram, a 10-wide bar and a 20-wide bar have the same frequency density of 2. How many more values are in the wider class?
- 16th August 1990Simplify sqrt(75) + sqrt(3), giving your answer in the form a sqrt(b).
- 17th August 1990Solve 12x^2 + 7x - 10 = 0.
- 18th August 1990A train slows steadily from 34 m/s to rest in 4 seconds. Work out its deceleration.
- 19th August 1990A cuboid measures 14 cm by 15 cm by 4 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 20th August 1990A bag holds 6 red and 5 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
- 21st August 1990A histogram has two bars: one 5 units wide with frequency density 1.5, one 20 units wide with density 3.5. How many values in total?
- 22nd August 1990A rectangle is 26 cm by 14 cm, each correct to the nearest cm. Work out the upper bound of its area.
- 23rd August 1990f(x) = 6x - 6. Work out the inverse function f^-1(x).
- 24th August 1990y is inversely proportional to x^2. When x = 2, y = 36. Work out y when x = 6.
- 25th August 1990A cuboid measures 13 cm by 5 cm by 6 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 26th August 1990A bag holds 5 red, 3 blue and 3 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 27th August 1990On a histogram, a 10-wide bar and a 30-wide bar have the same frequency density of 2. How many more values are in the wider class?
- 28th August 1990Expand and simplify (6 + sqrt(2))(6 - sqrt(2)).
- 29th August 1990Solve x^2 + y^2 = 841 and y = x - 1 simultaneously.
- 30th August 1990y is directly proportional to x^3. When x = 2, y = 16. Work out y when x = 5.
- 31st August 1990The 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.