Daily Practice · Higher Plus
June 1978 5-a-day
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The batch download puts all 5 tiers' June 1978 sheets in a single PDF, each tier behind its own divider page - 150 sheets in one file.
Every sheet in June 1978
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st June 1978A histogram has two bars: one 20 units wide with frequency density 0.4, one 5 units wide with density 1.4. How many values in total?
- 2nd June 1978Rationalise the denominator of 24/sqrt(6), giving your answer in its simplest form.
- 3rd June 1978The point (-1, -2) lies on y = f(x). Write down its image on y = f(x) + 2.
- 4th June 1978y is inversely proportional to x^2. When x = 3, y = 50. Work out y when x = 5.
- 5th June 1978The 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.
- 6th June 1978A bag holds 6 counters, r of them red. Two are taken without replacement and P(both red) = 2/5. Work out r.
- 7th June 1978On 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?
- 8th June 1978Simplify sqrt(27) + sqrt(147), giving your answer in the form a sqrt(b).
- 9th June 1978Prove that the sum of 4 consecutive integers is always a multiple of 2. State the simplified sum you would use.
- 10th June 1978y is directly proportional to x^3. When x = 2, y = 40. Work out y when x = 4.
- 11th June 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 June 1978The probability of winning a game is 1/4. A player expects 7 wins. How many games did they play?
- 13th June 1978A histogram has two bars: one 5 units wide with frequency density 1.5, one 20 units wide with density 1.4. How many values in total?
- 14th June 1978A rectangle is 17 cm by 25 cm, each correct to the nearest cm. Work out the upper bound of its area.
- 15th June 1978f(x) = 2x + 1 and g(x) = 4x + 4. Work out fg(-3).
- 16th June 1978y is directly proportional to sqrt(x). When x = 36, y = 30. Work out y when x = 64.
- 17th June 1978In a vector proof you find that vector PQ = a - 5b and vector RS = 3a - 15b. What does this show about PQ and RS?
- 18th June 1978A bag holds 7 red and n blue counters. The probability of taking a red is 7/10. Work out n.
- 19th June 1978On a histogram, a 10-wide bar and a 20-wide bar have the same frequency density of 3. How many more values are in the wider class?
- 20th June 1978Expand and simplify (9 + sqrt(10))(9 - sqrt(10)).
- 21st June 1978The curve y = sin x° is drawn for 0 <= x <= 360. Write down the value of y when x = 360.
- 22nd June 1978A train slows steadily from 16 m/s to rest in 8 seconds. Work out its deceleration.
- 23rd June 1978A cuboid measures 15 cm by 11 cm by 14 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 24th June 1978A bag holds 6 red and 8 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
- 25th June 1978A histogram has two bars: one 5 units wide with frequency density 2.5, one 5 units wide with density 0.6. How many values in total?
- 26th June 1978A block has mass 410 g (to the nearest 10 g) and volume 18 cm^3 (to the nearest cm^3). Work out the upper bound of its density, to 2 decimal places.
- 27th June 1978A quadratic sequence starts -2, -3, -2, 1. Work out the second difference, and the coefficient of n^2.
- 28th June 1978y is inversely proportional to x^2. When x = 3, y = 25. Work out y when x = 5.
- 29th June 1978A cuboid measures 5 cm by 7 cm by 10 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 30th June 1978A bag holds 6 red, 6 blue and 6 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?