Daily Practice · Higher Plus
January 1977 5-a-day
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The batch download puts all 5 tiers' January 1977 sheets in a single PDF, each tier behind its own divider page - 155 sheets in one file.
Every sheet in January 1977
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st January 1977A histogram has two bars: one 20 units wide with frequency density 2.5, one 25 units wide with density 0.6. How many values in total?
- 2nd January 1977x = 58 and y = 8, each correct to the nearest whole number. Work out the upper bound of x - y.
- 3rd January 1977Work out the nth term of the quadratic sequence 6, 23, 48, 81, ...
- 4th January 1977y is directly proportional to sqrt(x). When x = 9, y = 9. Work out y when x = 49.
- 5th January 1977A cuboid measures 14 cm by 4 cm by 4 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 6th January 1977A bag holds 3 red, 7 blue and 3 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 7th January 1977On 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?
- 8th January 1977A car covers 770 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.
- 9th January 1977The point (1, -4) lies on y = f(x). Write down its image on y = f(x) - 4.
- 10th January 1977A train slows steadily from 31 m/s to rest in 10 seconds. Work out its deceleration.
- 11th January 1977The point (9, 12) lies on the circle x^2 + y^2 = 225. Work out the gradient of the tangent to the circle at that point.
- 12th January 1977A bag holds 5 counters, r of them red. Two are taken without replacement and P(both red) = 3/10. Work out r.
- 13th January 1977A histogram has two bars: one 5 units wide with frequency density 1.5, one 20 units wide with density 3.5. How many values in total?
- 14th January 1977Rationalise the denominator of 72/sqrt(6), giving your answer in its simplest form.
- 15th January 1977Prove that the sum of 7 consecutive integers is always a multiple of 7. State the simplified sum you would use.
- 16th January 1977y is inversely proportional to x^2. When x = 2, y = 50. Work out y when x = 5.
- 17th January 1977In 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.
- 18th January 1977The probability of winning a game is 2/5. A player expects 28 wins. How many games did they play?
- 19th January 1977On 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?
- 20th January 1977Simplify sqrt(20) + sqrt(125), giving your answer in the form a sqrt(b).
- 21st January 1977f(x) = 2x - 6 and g(x) = 3x + 1. Work out fg(-2).
- 22nd January 1977y is directly proportional to x^3. When x = 3, y = 162. Work out y when x = 4.
- 23rd January 1977In a vector proof you find that vector PQ = 4a + 4b and vector RS = 20a + 20b. What does this show about PQ and RS?
- 24th January 1977A bag holds 7 red and n blue counters. The probability of taking a red is 1/2. Work out n.
- 25th January 1977A histogram has two bars: one 20 units wide with frequency density 2, one 20 units wide with density 3. How many values in total?
- 26th January 1977A rectangle is 24 cm by 13 cm, each correct to the nearest cm. Work out the upper bound of its area.
- 27th January 1977The curve y = cos x° is drawn for 0 <= x <= 360. Write down the value of y when x = 0.
- 28th January 1977y is directly proportional to sqrt(x). When x = 49, y = 14. Work out y when x = 81.
- 29th January 1977A cuboid measures 7 cm by 15 cm by 7 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 30th January 1977A bag holds 5 red and 5 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
- 31st January 1977On 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?