Daily Practice · Higher Plus
August 1989 5-a-day
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The batch download puts all 5 tiers' August 1989 sheets in a single PDF, each tier behind its own divider page - 155 sheets in one file.
Every sheet in August 1989
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st August 1989A bag holds 4 red, 4 blue and 5 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 2nd August 1989A histogram has two bars: one 10 units wide with frequency density 0.4, one 25 units wide with density 3.5. How many values in total?
- 3rd August 1989Simplify sqrt(50) + sqrt(72), giving your answer in the form a sqrt(b).
- 4th August 1989The point (0, 2) lies on y = f(x). Write down its image on y = f(x - 2).
- 5th August 1989y is inversely proportional to x^2. When x = 2, y = 72. Work out y when x = 6.
- 6th August 1989The 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.
- 7th August 1989A bag holds 7 counters, r of them red. Two are taken without replacement and P(both red) = 2/7. Work out r.
- 8th August 1989On a histogram, a 10-wide bar and a 40-wide bar have the same frequency density of 1.5. How many more values are in the wider class?
- 9th August 1989A rectangle is 23 cm by 8 cm, each correct to the nearest cm. Work out the upper bound of its area.
- 10th August 1989Prove that the sum of 5 consecutive integers is always a multiple of 5. State the simplified sum you would use.
- 11th August 1989y is directly proportional to x^3. When x = 2, y = 24. Work out y when x = 4.
- 12th August 1989In a circle theorem proof, a step uses the fact that the exterior angle of a cyclic quadrilateral is being found. State the reason being quoted.
- 13th August 1989The probability of winning a game is 2/5. A player expects 10 wins. How many games did they play?
- 14th August 1989A histogram has two bars: one 20 units wide with frequency density 2.5, one 20 units wide with density 3.5. How many values in total?
- 15th August 1989Expand and simplify (4 + sqrt(10))(4 - sqrt(10)).
- 16th August 1989f(x) = 5x - 7 and g(x) = 6x + 5. Work out fg(2).
- 17th August 1989y is directly proportional to sqrt(x). When x = 4, y = 18. Work out y when x = 81.
- 18th August 1989In a vector proof you find that vector PQ = a - b and vector RS = 4a - 4b. What does this show about PQ and RS?
- 19th August 1989A bag holds 7 red and n blue counters. The probability of taking a red is 7/13. Work out n.
- 20th August 1989On a histogram, a 4-wide bar and a 16-wide bar have the same frequency density of 1.5. How many more values are in the wider class?
- 21st August 1989A block has mass 620 g (to the nearest 10 g) and volume 13 cm^3 (to the nearest cm^3). Work out the upper bound of its density, to 2 decimal places.
- 22nd August 1989The curve y = cos x° is drawn for 0 <= x <= 360. Write down the value of y when x = 0.
- 23rd August 1989A train slows steadily from 24 m/s to rest in 5 seconds. Work out its deceleration.
- 24th August 1989A cuboid measures 15 cm by 4 cm by 9 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 25th August 1989A bag holds 3 red and 5 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
- 26th August 1989A histogram has two bars: one 20 units wide with frequency density 2, one 5 units wide with density 3.5. How many values in total?
- 27th August 1989x = 146 and y = 77, each correct to the nearest whole number. Work out the upper bound of x - y.
- 28th August 1989A quadratic sequence starts 12, 29, 54, 87. Work out the second difference, and the coefficient of n^2.
- 29th August 1989y is inversely proportional to x^2. When x = 3, y = 72. Work out y when x = 6.
- 30th August 1989A cuboid measures 7 cm by 5 cm by 6 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 31st August 1989A bag holds 5 red, 7 blue and 6 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?