Daily Practice · Higher Plus
August 1978 5-a-day
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The batch download puts all 5 tiers' August 1978 sheets in a single PDF, each tier behind its own divider page - 155 sheets in one file.
Every sheet in August 1978
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st August 1978Expand and simplify (8 + sqrt(11))(8 - sqrt(11)).
- 2nd August 1978Make x the subject of 3x + 6 = y(x + 6).
- 3rd August 1978y is directly proportional to sqrt(x). When x = 25, y = 25. Work out y when x = 81.
- 4th August 1978The point (20, 21) lies on the circle x^2 + y^2 = 841. Work out the gradient of the tangent to the circle at that point.
- 5th August 1978A bag holds 8 counters, r of them red. Two are taken without replacement and P(both red) = 5/14. Work out r.
- 6th August 1978On 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?
- 7th August 1978A block has mass 310 g (to the nearest 10 g) and volume 24 cm^3 (to the nearest cm^3). Work out the upper bound of its density, to 2 decimal places.
- 8th August 1978Write 6/(x - 6) + 7/(x + 3) as a single fraction.
- 9th August 1978A train slows steadily from 17 m/s to rest in 4 seconds. Work out its deceleration.
- 10th August 1978In 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.
- 11th August 1978The probability of winning a game is 1/4. A player expects 3 wins. How many games did they play?
- 12th August 1978A histogram has two bars: one 5 units wide with frequency density 2.5, one 20 units wide with density 0.6. How many values in total?
- 13th August 1978x = 84 and y = 53, each correct to the nearest whole number. Work out the upper bound of x - y.
- 14th August 1978Solve 2x^2 + 3x - 9 = 0.
- 15th August 1978y is inversely proportional to x^2. When x = 2, y = 48. Work out y when x = 4.
- 16th August 1978In a vector proof you find that vector PQ = 4a + 4b and vector RS = 12a + 12b. What does this show about PQ and RS?
- 17th August 1978A bag holds 4 red and n blue counters. The probability of taking a red is 4/11. Work out n.
- 18th August 1978On a histogram, a 4-wide bar and a 8-wide bar have the same frequency density of 3. How many more values are in the wider class?
- 19th August 1978A car covers 640 m (to the nearest 10 m) in 4 s (to the nearest second). Work out the lower bound of its speed, to 2 decimal places.
- 20th August 1978f(x) = 7x + 7. Work out the inverse function f^-1(x).
- 21st August 1978y is directly proportional to x^3. When x = 2, y = 32. Work out y when x = 4.
- 22nd August 1978A cuboid measures 11 cm by 9 cm by 8 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 23rd August 1978A bag holds 8 red and 3 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
- 24th August 1978A histogram has two bars: one 10 units wide with frequency density 1.2, one 25 units wide with density 1.4. How many values in total?
- 25th August 1978Rationalise the denominator of 72/sqrt(6), giving your answer in its simplest form.
- 26th August 1978Solve x^2 + y^2 = 625 and y = x - 17 simultaneously.
- 27th August 1978y is directly proportional to sqrt(x). When x = 16, y = 16. Work out y when x = 81.
- 28th August 1978A cuboid measures 6 cm by 10 cm by 14 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 29th August 1978A bag holds 7 red, 3 blue and 4 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 30th August 1978On a histogram, a 5-wide bar and a 15-wide bar have the same frequency density of 1.5. How many more values are in the wider class?
- 31st August 1978Simplify sqrt(8) + sqrt(18), giving your answer in the form a sqrt(b).