Daily Practice · Higher Plus
July 1976 5-a-day
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The batch download puts all 5 tiers' July 1976 sheets in a single PDF, each tier behind its own divider page - 155 sheets in one file.
Every sheet in July 1976
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st July 1976f(x) = 2x - 5 and g(x) = 3x - 6. Work out fg(4).
- 2nd July 1976A train slows steadily from 35 m/s to rest in 10 seconds. Work out its deceleration.
- 3rd July 1976A cuboid measures 8 cm by 9 cm by 11 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 4th July 1976A bag holds 4 red and 6 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
- 5th July 1976A histogram has two bars: one 20 units wide with frequency density 1.5, one 20 units wide with density 3. How many values in total?
- 6th July 1976Expand and simplify (2 + sqrt(5))(2 - sqrt(5)).
- 7th July 1976The curve y = cos x° is drawn for 0 <= x <= 360. Write down the value of y when x = 0.
- 8th July 1976y is inversely proportional to x^2. When x = 2, y = 108. Work out y when x = 6.
- 9th July 1976A cuboid measures 7 cm by 10 cm by 4 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 10th July 1976A bag holds 7 red, 3 blue and 3 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 11th July 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?
- 12th July 1976A block has mass 770 g (to the nearest 10 g) and volume 17 cm^3 (to the nearest cm^3). Work out the upper bound of its density, to 2 decimal places.
- 13th July 1976A quadratic sequence starts 5, 23, 51, 89. Work out the second difference, and the coefficient of n^2.
- 14th July 1976y is directly proportional to x^3. When x = 4, y = 256. Work out y when x = 3.
- 15th July 1976The point (12, 16) lies on the circle x^2 + y^2 = 400. Work out the gradient of the tangent to the circle at that point.
- 16th July 1976A bag holds 5 counters, r of them red. Two are taken without replacement and P(both red) = 1/10. Work out r.
- 17th July 1976A histogram has two bars: one 20 units wide with frequency density 0.4, one 25 units wide with density 0.6. How many values in total?
- 18th July 1976x = 102 and y = 51, each correct to the nearest whole number. Work out the upper bound of x - y.
- 19th July 1976Solve x^2 + 12x + 35 > 0.
- 20th July 1976y is directly proportional to sqrt(x). When x = 49, y = 21. Work out y when x = 36.
- 21st July 1976In a circle theorem proof, a step uses the fact that the exterior angle of a cyclic quadrilateral is being found. State the reason being quoted.
- 22nd July 1976The probability of winning a game is 1/2. A player expects 16 wins. How many games did they play?
- 23rd July 1976On a histogram, a 4-wide bar and a 16-wide bar have the same frequency density of 1.5. How many more values are in the wider class?
- 24th July 1976A car covers 290 m (to the nearest 10 m) in 6 s (to the nearest second). Work out the lower bound of its speed, to 2 decimal places.
- 25th July 1976Write x^2 + 10x - 13 in the form (x + a)^2 + b.
- 26th July 1976A train slows steadily from 29 m/s to rest in 4 seconds. Work out its deceleration.
- 27th July 1976In a vector proof you find that vector PQ = 3a + 3b and vector RS = 15a + 15b. What does this show about PQ and RS?
- 28th July 1976A bag holds 8 red and n blue counters. The probability of taking a red is 4/7. Work out n.
- 29th July 1976A histogram has two bars: one 5 units wide with frequency density 2, one 20 units wide with density 0.8. How many values in total?
- 30th July 1976Rationalise the denominator of 72/sqrt(6), giving your answer in its simplest form.
- 31st July 1976Work out the coordinates of the turning point of y = x^2 + 10x - 3.