Daily Practice · Higher Plus
September 1976 5-a-day
Printing for a group?
The batch download puts all 5 tiers' September 1976 sheets in a single PDF, each tier behind its own divider page - 150 sheets in one file.
Every sheet in September 1976
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st September 1976A cuboid measures 5 cm by 9 cm by 12 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 2nd September 1976A bag holds 8 red and 6 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
- 3rd September 1976A histogram has two bars: one 20 units wide with frequency density 1.5, one 20 units wide with density 1.4. How many values in total?
- 4th September 1976A car covers 900 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.
- 5th September 1976f(x) = 3x + 12. Work out the inverse function f^-1(x).
- 6th September 1976y is directly proportional to sqrt(x). When x = 36, y = 54. Work out y when x = 9.
- 7th September 1976A cuboid measures 8 cm by 7 cm by 7 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 8th September 1976A bag holds 4 red, 3 blue and 5 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 9th September 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?
- 10th September 1976Rationalise the denominator of 70/sqrt(7), giving your answer in its simplest form.
- 11th September 1976Solve x^2 + y^2 = 676 and y = x - 14 simultaneously.
- 12th September 1976A train slows steadily from 13 m/s to rest in 4 seconds. Work out its deceleration.
- 13th September 1976The point (6, 8) lies on the circle x^2 + y^2 = 100. Work out the gradient of the tangent to the circle at that point.
- 14th September 1976A bag holds 6 counters, r of them red. Two are taken without replacement and P(both red) = 2/5. Work out r.
- 15th September 1976A histogram has two bars: one 5 units wide with frequency density 1.2, one 10 units wide with density 3.5. How many values in total?
- 16th September 1976Simplify sqrt(12) + sqrt(27), giving your answer in the form a sqrt(b).
- 17th September 1976Use the iteration x(n+1) = cube root of (11x(n) + 3) with x(0) = 1. Work out x(1) to 3 decimal places.
- 18th September 1976y is inversely proportional to x^2. When x = 4, y = 50. Work out y when x = 5.
- 19th September 1976In a circle theorem proof, a step uses the fact that two tangents are drawn to a circle from the same external point. State the reason being quoted.
- 20th September 1976The probability of winning a game is 1/2. A player expects 15 wins. How many games did they play?
- 21st September 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?
- 22nd September 1976A rectangle is 7 cm by 21 cm, each correct to the nearest cm. Work out the upper bound of its area.
- 23rd September 1976Work out the nth term of the quadratic sequence -4, 3, 16, 35, ...
- 24th September 1976y is directly proportional to x^3. When x = 4, y = 128. Work out y when x = 2.
- 25th September 1976In a vector proof you find that vector PQ = 3a + 3b and vector RS = 6a + 6b. What does this show about PQ and RS?
- 26th September 1976A bag holds 4 red and n blue counters. The probability of taking a red is 2/5. Work out n.
- 27th September 1976A histogram has two bars: one 10 units wide with frequency density 1.2, one 5 units wide with density 0.6. How many values in total?
- 28th September 1976Expand and simplify (6 + sqrt(10))(6 - sqrt(10)).
- 29th September 1976The point (1, -6) lies on y = f(x). Write down its image on y = f(x + 4).
- 30th September 1976y is directly proportional to sqrt(x). When x = 25, y = 35. Work out y when x = 9.