Daily Practice · Higher Plus
January 1976 5-a-day
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The batch download puts all 5 tiers' January 1976 sheets in a single PDF, each tier behind its own divider page - 155 sheets in one file.
Every sheet in January 1976
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st January 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?
- 2nd January 1976Rationalise the denominator of 30/sqrt(6), giving your answer in its simplest form.
- 3rd January 1976Write x^2 - 10x + 1 in the form (x + a)^2 + b.
- 4th January 1976y is directly proportional to x^3. When x = 4, y = 192. Work out y when x = 5.
- 5th January 1976A cuboid measures 12 cm by 4 cm by 9 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 6th January 1976A bag holds 5 red and 8 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
- 7th January 1976A histogram has two bars: one 10 units wide with frequency density 2.5, one 10 units wide with density 1.4. How many values in total?
- 8th January 1976Simplify sqrt(32) + sqrt(32), giving your answer in the form a sqrt(b).
- 9th January 1976Work out the coordinates of the turning point of y = x^2 - 14x + 6.
- 10th January 1976y is directly proportional to sqrt(x). When x = 4, y = 10. Work out y when x = 25.
- 11th January 1976A cuboid measures 6 cm by 10 cm by 8 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 12th January 1976A bag holds 6 red, 5 blue and 2 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 13th January 1976On a histogram, a 5-wide bar and a 20-wide bar have the same frequency density of 1.5. How many more values are in the wider class?
- 14th January 1976A rectangle is 16 cm by 16 cm, each correct to the nearest cm. Work out the upper bound of its area.
- 15th January 1976Simplify (x^2 + x - 30)/(x + 6).
- 16th January 1976A train slows steadily from 35 m/s to rest in 4 seconds. Work out its deceleration.
- 17th January 1976The point (20, 21) lies on the circle x^2 + y^2 = 841. Work out the gradient of the tangent to the circle at that point.
- 18th January 1976A bag holds 10 counters, r of them red. Two are taken without replacement and P(both red) = 2/9. Work out r.
- 19th January 1976A histogram has two bars: one 5 units wide with frequency density 0.4, one 20 units wide with density 3.5. How many values in total?
- 20th January 1976Expand and simplify (7 + sqrt(11))(7 - sqrt(11)).
- 21st January 1976In an algebraic proof, how would you write three consecutive integers in terms of an integer n?
- 22nd January 1976y is inversely proportional to x^2. When x = 2, y = 18. Work out y when x = 3.
- 23rd January 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.
- 24th January 1976The probability of winning a game is 3/4. A player expects 30 wins. How many games did they play?
- 25th January 1976On a histogram, a 5-wide bar and a 20-wide bar have the same frequency density of 3. How many more values are in the wider class?
- 26th January 1976A block has mass 280 g (to the nearest 10 g) and volume 10 cm^3 (to the nearest cm^3). Work out the upper bound of its density, to 2 decimal places.
- 27th January 1976Make x the subject of 8x + 3 = y(x + 3).
- 28th January 1976y is directly proportional to x^3. When x = 2, y = 32. Work out y when x = 3.
- 29th January 1976In a vector proof you find that vector PQ = 5a - 3b and vector RS = 25a - 15b. What does this show about PQ and RS?
- 30th January 1976A bag holds 7 red and n blue counters. The probability of taking a red is 7/15. Work out n.
- 31st January 1976A histogram has two bars: one 5 units wide with frequency density 1.2, one 25 units wide with density 0.8. How many values in total?