Daily Practice · Higher Plus
July 1978 5-a-day
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The batch download puts all 5 tiers' July 1978 sheets in a single PDF, each tier behind its own divider page - 155 sheets in one file.
Every sheet in July 1978
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st July 1978On a histogram, a 10-wide bar and a 30-wide bar have the same frequency density of 1.5. How many more values are in the wider class?
- 2nd July 1978x = 167 and y = 112, each correct to the nearest whole number. Work out the upper bound of x - y.
- 3rd July 1978Solve x^2 - 4x < 0.
- 4th July 1978y is directly proportional to x^3. When x = 4, y = 256. Work out y when x = 3.
- 5th July 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.
- 6th July 1978A bag holds 7 counters, r of them red. Two are taken without replacement and P(both red) = 2/7. Work out r.
- 7th July 1978A histogram has two bars: one 10 units wide with frequency density 1.2, one 5 units wide with density 3. How many values in total?
- 8th July 1978A car covers 880 m (to the nearest 10 m) in 9 s (to the nearest second). Work out the lower bound of its speed, to 2 decimal places.
- 9th July 1978Write x^2 + 14x + 5 in the form (x + a)^2 + b.
- 10th July 1978y is directly proportional to sqrt(x). When x = 36, y = 36. Work out y when x = 64.
- 11th July 1978In a circle theorem proof, a step uses the fact that OA and OB are both radii of the circle, so triangle OAB is isosceles. State the reason being quoted.
- 12th July 1978The probability of winning a game is 4/5. A player expects 104 wins. How many games did they play?
- 13th July 1978On a histogram, a 10-wide bar and a 30-wide bar have the same frequency density of 3. How many more values are in the wider class?
- 14th July 1978Rationalise the denominator of 18/sqrt(3), giving your answer in its simplest form.
- 15th July 1978Work out the coordinates of the turning point of y = x^2 - 10x - 15.
- 16th July 1978A train slows steadily from 31 m/s to rest in 8 seconds. Work out its deceleration.
- 17th July 1978In a vector proof you find that vector PQ = 4a - 4b and vector RS = 16a - 16b. What does this show about PQ and RS?
- 18th July 1978A bag holds 3 red and n blue counters. The probability of taking a red is 1/3. Work out n.
- 19th July 1978A histogram has two bars: one 10 units wide with frequency density 2.5, one 5 units wide with density 1.4. How many values in total?
- 20th July 1978Simplify sqrt(18) + sqrt(2), giving your answer in the form a sqrt(b).
- 21st July 1978Simplify (x^2 - 12x + 32)/(x - 8).
- 22nd July 1978y is inversely proportional to x^2. When x = 5, y = 32. Work out y when x = 4.
- 23rd July 1978A cuboid measures 8 cm by 10 cm by 4 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 24th July 1978A bag holds 4 red and 6 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
- 25th July 1978On 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?
- 26th July 1978A rectangle is 20 cm by 14 cm, each correct to the nearest cm. Work out the upper bound of its area.
- 27th July 1978In an algebraic proof, how would you write the next even number after 2n in terms of an integer n?
- 28th July 1978y is directly proportional to x^3. When x = 2, y = 32. Work out y when x = 4.
- 29th July 1978A cuboid measures 4 cm by 11 cm by 8 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 30th July 1978A bag holds 7 red, 3 blue and 2 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 31st July 1978A histogram has two bars: one 5 units wide with frequency density 2, one 20 units wide with density 3. How many values in total?