Daily Practice · Higher Plus
December 1976 5-a-day
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The batch download puts all 5 tiers' December 1976 sheets in a single PDF, each tier behind its own divider page - 155 sheets in one file.
Every sheet in December 1976
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st December 1976A bag holds 3 red and 10 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
- 2nd December 1976On a histogram, a 10-wide bar and a 40-wide bar have the same frequency density of 2. How many more values are in the wider class?
- 3rd December 1976Rationalise the denominator of 48/sqrt(6), giving your answer in its simplest form.
- 4th December 1976Write 7/(x - 1) + 5/(x - 5) as a single fraction.
- 5th December 1976y is directly proportional to x^3. When x = 2, y = 16. Work out y when x = 3.
- 6th December 1976A cuboid measures 9 cm by 8 cm by 7 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 7th December 1976A bag holds 6 red, 3 blue and 4 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 8th December 1976A histogram has two bars: one 10 units wide with frequency density 1.2, one 20 units wide with density 0.8. How many values in total?
- 9th December 1976Simplify sqrt(45) + sqrt(5), giving your answer in the form a sqrt(b).
- 10th December 1976Solve 12x^2 + 7x - 12 = 0.
- 11th December 1976y is directly proportional to sqrt(x). When x = 49, y = 14. Work out y when x = 9.
- 12th December 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.
- 13th December 1976A bag holds 5 counters, r of them red. Two are taken without replacement and P(both red) = 3/10. Work out r.
- 14th December 1976On a histogram, a 10-wide bar and a 40-wide bar have the same frequency density of 2.5. How many more values are in the wider class?
- 15th December 1976A rectangle is 11 cm by 19 cm, each correct to the nearest cm. Work out the upper bound of its area.
- 16th December 1976f(x) = 2x + 9. Work out the inverse function f^-1(x).
- 17th December 1976A train slows steadily from 39 m/s to rest in 10 seconds. Work out its deceleration.
- 18th December 1976In a circle theorem proof, a step uses the fact that the three angles of triangle OAB are being summed. State the reason being quoted.
- 19th December 1976The probability of winning a game is 4/5. A player expects 24 wins. How many games did they play?
- 20th December 1976A histogram has two bars: one 5 units wide with frequency density 2.5, one 20 units wide with density 0.8. How many values in total?
- 21st December 1976Expand and simplify (5 + sqrt(2))(5 - sqrt(2)).
- 22nd December 1976Solve x^2 + y^2 = 841 and y = x - 1 simultaneously.
- 23rd December 1976y is inversely proportional to x^2. When x = 4, y = 25. Work out y when x = 5.
- 24th December 1976In a vector proof you find that vector PQ = 4a - 3b and vector RS = 16a - 12b. What does this show about PQ and RS?
- 25th December 1976A bag holds 6 red and n blue counters. The probability of taking a red is 6/13. Work out n.
- 26th December 1976On 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?
- 27th December 1976A block has mass 720 g (to the nearest 10 g) and volume 19 cm^3 (to the nearest cm^3). Work out the upper bound of its density, to 2 decimal places.
- 28th December 1976Use the iteration x(n+1) = cube root of (9x(n) + 5) with x(0) = 3. Work out x(1) to 3 decimal places.
- 29th December 1976y is directly proportional to x^3. When x = 2, y = 40. Work out y when x = 3.
- 30th December 1976A cuboid measures 7 cm by 5 cm by 12 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 31st December 1976A bag holds 5 red and 6 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?