Daily Practice · Higher Plus
June 1976 5-a-day
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The batch download puts all 5 tiers' June 1976 sheets in a single PDF, each tier behind its own divider page - 150 sheets in one file.
Every sheet in June 1976
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st June 1976Solve x^2 + y^2 = 25 and y = x + 1 simultaneously.
- 2nd June 1976y is directly proportional to sqrt(x). When x = 16, y = 12. Work out y when x = 49.
- 3rd June 1976A cuboid measures 5 cm by 15 cm by 12 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 4th June 1976A bag holds 6 red and 3 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
- 5th June 1976On 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?
- 6th June 1976x = 182 and y = 149, each correct to the nearest whole number. Work out the upper bound of x - y.
- 7th June 1976Use the iteration x(n+1) = cube root of (2x(n) + 4) with x(0) = 5. Work out x(1) to 3 decimal places.
- 8th June 1976A train slows steadily from 32 m/s to rest in 8 seconds. Work out its deceleration.
- 9th June 1976A cuboid measures 4 cm by 9 cm by 6 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 10th June 1976A bag holds 4 red, 6 blue and 6 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 11th June 1976A histogram has two bars: one 10 units wide with frequency density 2, one 25 units wide with density 0.8. How many values in total?
- 12th June 1976A car covers 270 m (to the nearest 10 m) in 8 s (to the nearest second). Work out the lower bound of its speed, to 2 decimal places.
- 13th June 1976Work out the nth term of the quadratic sequence 9, 17, 31, 51, ...
- 14th June 1976y is inversely proportional to x^2. When x = 3, y = 75. Work out y when x = 5.
- 15th June 1976The point (8, 15) lies on the circle x^2 + y^2 = 289. Work out the gradient of the tangent to the circle at that point.
- 16th June 1976A bag holds 6 counters, r of them red. Two are taken without replacement and P(both red) = 1/15. Work out r.
- 17th June 1976On a histogram, a 5-wide bar and a 15-wide bar have the same frequency density of 2.5. How many more values are in the wider class?
- 18th June 1976Rationalise the denominator of 66/sqrt(6), giving your answer in its simplest form.
- 19th June 1976The point (0, -3) lies on y = f(x). Write down its image on y = f(-x).
- 20th June 1976y is directly proportional to x^3. When x = 2, y = 40. Work out y when x = 5.
- 21st June 1976In a circle theorem proof, a step uses the fact that a triangle is drawn from the ends of a diameter to a point on the circle. State the reason being quoted.
- 22nd June 1976The probability of winning a game is 2/5. A player expects 16 wins. How many games did they play?
- 23rd June 1976A histogram has two bars: one 20 units wide with frequency density 2, one 10 units wide with density 0.6. How many values in total?
- 24th June 1976Simplify sqrt(18) + sqrt(2), giving your answer in the form a sqrt(b).
- 25th June 1976Prove that the sum of 7 consecutive integers is always a multiple of 7. State the simplified sum you would use.
- 26th June 1976y is directly proportional to sqrt(x). When x = 25, y = 10. Work out y when x = 36.
- 27th June 1976In a vector proof you find that vector PQ = a - 2b and vector RS = 4a - 8b. What does this show about PQ and RS?
- 28th June 1976A bag holds 5 red and n blue counters. The probability of taking a red is 5/12. Work out n.
- 29th June 1976On a histogram, a 4-wide bar and a 12-wide bar have the same frequency density of 1.5. How many more values are in the wider class?
- 30th June 1976A rectangle is 24 cm by 18 cm, each correct to the nearest cm. Work out the upper bound of its area.