Zadanie 7a
Find k for which there are infinitely many solutions.
Linear systems and solution sets
Solve systems of up to three linear equations, distinguish inconsistent and dependent cases, and express general solutions.
Tę umiejętność sprawdza 12 zadań wzorowanych na arkuszach IB z lat 2022–2026.
Zadania sprawdzające tę umiejętność: 12 Otwórz w wyszukiwarce z filtrami
Zadanie 7b
For this k, (i) interpret the solutions geometrically; (ii) express them parametrically.
Zadanie 10a
Show that a=1 and b=−6.
Zadanie 2
Let F(x) = 3x4 − 4x3 + px2 + qx + 1. The polynomial has factor x + 1, and division by x − 2 leaves remainder 45. Determine p and q.
Zadanie 9b
Three planes are P1 : 2x − y + z = 0, P2 : x + by + 2z = 5 and P3 : 3x + y + 3z = d, where b, d > 0. They have a common line. Find b and d.
Zadanie 6
Find integer α,β for which the system x − 2z = 3, 3x + 2y + z = 19, 2x + 2y + αz = β has infinitely many solutions.
Zadanie 7a
Give the general solution of the first two equations in parametric form.
Zadanie 7b
For a=4,k=20, find the unique solution of all three equations.
Zadanie 7c
(i) State a for which the system has no unique solution. (ii) For this a, state k giving infinitely many solutions.
Zadanie 9
The curve y = (x + 2)/(ax2 + bx + c) has a local minimum at (1,2) and a vertical asymptote x=−1. The real constants a,b,c are nonzero. Find them.
Zadanie 2c
Solve E_a and H_b simultaneously to show that their four intersections have coordinates , where the two signs are independent.
Zadanie 1b
For n=1,2,3, the values of S2(n) are 1,10,p. (i) State p. (ii) Suppose S2(n) = a1n + a2n2 + a3n3 for rational coefficients a₁,a₂,a₃. Write three linear equations for these coefficients. (iii) Hence determine the coefficients.