Daily Practice · Higher Plus
August 1976 5-a-day
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The batch download puts all 5 tiers' August 1976 sheets in a single PDF, each tier behind its own divider page - 155 sheets in one file.
Every sheet in August 1976
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st August 1976y is inversely proportional to x^2. When x = 3, y = 72. Work out y when x = 6.
- 2nd August 1976A cuboid measures 12 cm by 12 cm by 12 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 3rd August 1976A bag holds 4 red and 4 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
- 4th August 1976On a histogram, a 4-wide bar and a 12-wide bar have the same frequency density of 2. How many more values are in the wider class?
- 5th August 1976Simplify sqrt(80) + sqrt(80), giving your answer in the form a sqrt(b).
- 6th August 1976Simplify (x^2 + 10x + 24)/(x + 6).
- 7th August 1976y is directly proportional to x^3. When x = 4, y = 384. Work out y when x = 2.
- 8th August 1976A cuboid measures 5 cm by 13 cm by 13 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 9th August 1976A bag holds 4 red, 6 blue and 4 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 10th August 1976A histogram has two bars: one 20 units wide with frequency density 1.5, one 20 units wide with density 3.5. How many values in total?
- 11th August 1976A rectangle is 23 cm by 6 cm, each correct to the nearest cm. Work out the upper bound of its area.
- 12th August 1976In an algebraic proof, how would you write the square of an odd number in terms of an integer n?
- 13th August 1976y is directly proportional to sqrt(x). When x = 16, y = 20. Work out y when x = 64.
- 14th August 1976The point (3, 4) lies on the circle x^2 + y^2 = 25. Work out the gradient of the tangent to the circle at that point.
- 15th August 1976A bag holds 6 counters, r of them red. Two are taken without replacement and P(both red) = 2/5. Work out r.
- 16th August 1976On a histogram, a 5-wide bar and a 15-wide bar have the same frequency density of 2. How many more values are in the wider class?
- 17th August 1976Expand and simplify (3 + sqrt(10))(3 - sqrt(10)).
- 18th August 1976Make x the subject of 2x + 8 = y(x + 8).
- 19th August 1976A train slows steadily from 35 m/s to rest in 8 seconds. Work out its deceleration.
- 20th August 1976In a circle theorem proof, a step uses the fact that a radius is drawn to the midpoint of a chord. State the reason being quoted.
- 21st August 1976The probability of winning a game is 1/4. A player expects 10 wins. How many games did they play?
- 22nd August 1976A histogram has two bars: one 10 units wide with frequency density 2.5, one 25 units wide with density 0.8. How many values in total?
- 23rd August 1976A block has mass 860 g (to the nearest 10 g) and volume 23 cm^3 (to the nearest cm^3). Work out the upper bound of its density, to 2 decimal places.
- 24th August 1976Write 4/(x + 1) + 6/(x + 5) as a single fraction.
- 25th August 1976y is inversely proportional to x^2. When x = 4, y = 16. Work out y when x = 2.
- 26th August 1976In a vector proof you find that vector PQ = a + 6b and vector RS = 2a + 12b. What does this show about PQ and RS?
- 27th August 1976A bag holds 6 red and n blue counters. The probability of taking a red is 3/7. Work out n.
- 28th August 1976On a histogram, a 5-wide bar and a 10-wide bar have the same frequency density of 1.5. How many more values are in the wider class?
- 29th August 1976x = 41 and y = 15, each correct to the nearest whole number. Work out the upper bound of x - y.
- 30th August 1976Solve 5x^2 + 18x - 8 = 0.
- 31st August 1976y is directly proportional to x^3. When x = 4, y = 320. Work out y when x = 5.