Daily Practice · Higher Plus
June 1975 5-a-day
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The batch download puts all 5 tiers' June 1975 sheets in a single PDF, each tier behind its own divider page - 150 sheets in one file.
Every sheet in June 1975
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st June 1975A quadratic sequence starts 11, 18, 27, 38. Work out the second difference, and the coefficient of n^2.
- 2nd June 1975y is directly proportional to x^3. When x = 2, y = 40. Work out y when x = 5.
- 3rd June 1975In a vector proof you find that vector PQ = 2a - 2b and vector RS = 4a - 4b. What does this show about PQ and RS?
- 4th June 1975A bag holds 3 red and n blue counters. The probability of taking a red is 3/7. Work out n.
- 5th June 1975A histogram has two bars: one 5 units wide with frequency density 1.2, one 10 units wide with density 3. How many values in total?
- 6th June 1975Rationalise the denominator of 77/sqrt(11), giving your answer in its simplest form.
- 7th June 1975Solve x^2 + 7x > 0.
- 8th June 1975y is directly proportional to sqrt(x). When x = 16, y = 32. Work out y when x = 49.
- 9th June 1975A cuboid measures 12 cm by 4 cm by 13 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 10th June 1975A bag holds 5 red and 9 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
- 11th June 1975On a histogram, a 10-wide bar and a 30-wide bar have the same frequency density of 2.5. How many more values are in the wider class?
- 12th June 1975Simplify sqrt(12) + sqrt(75), giving your answer in the form a sqrt(b).
- 13th June 1975Write x^2 + 2x + 1 in the form (x + a)^2 + b.
- 14th June 1975A train slows steadily from 35 m/s to rest in 5 seconds. Work out its deceleration.
- 15th June 1975A cuboid measures 14 cm by 5 cm by 8 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 16th June 1975A bag holds 7 red, 7 blue and 2 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 17th June 1975A histogram has two bars: one 10 units wide with frequency density 2, one 25 units wide with density 1.4. How many values in total?
- 18th June 1975A rectangle is 20 cm by 28 cm, each correct to the nearest cm. Work out the upper bound of its area.
- 19th June 1975Work out the coordinates of the turning point of y = x^2 + 4x + 6.
- 20th June 1975y is inversely proportional to x^2. When x = 4, y = 144. Work out y when x = 6.
- 21st June 1975The 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.
- 22nd June 1975A bag holds 6 counters, r of them red. Two are taken without replacement and P(both red) = 2/5. Work out r.
- 23rd June 1975On a histogram, a 4-wide bar and a 8-wide bar have the same frequency density of 2. How many more values are in the wider class?
- 24th June 1975Expand and simplify (3 + sqrt(11))(3 - sqrt(11)).
- 25th June 1975Simplify (x^2 - 2x - 15)/(x - 5).
- 26th June 1975y is directly proportional to x^3. When x = 4, y = 384. Work out y when x = 3.
- 27th June 1975In a circle theorem proof, a step uses the fact that the angle in a semicircle is being proved. State the reason being quoted.
- 28th June 1975The probability of winning a game is 1/10. A player expects 5 wins. How many games did they play?
- 29th June 1975A histogram has two bars: one 5 units wide with frequency density 0.4, one 5 units wide with density 1.4. How many values in total?
- 30th June 1975A block has mass 510 g (to the nearest 10 g) and volume 21 cm^3 (to the nearest cm^3). Work out the upper bound of its density, to 2 decimal places.